Problem: Rewrite as a simplified fraction. ${0.9\overline{34} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 934.3434...\\ 10x &= 9.3434...\end{align*}}$ Subtracting the two equations, we have: ${990x = 925}$ ${x = \dfrac{925}{990}} $ ${x = \dfrac{185}{198}} $